Torques of equal magnitude are applied to a hollow cylinder and a solid sphere, both having the same mass and radius. The cylinder is free to rotate about its standard axis of symmetry and the sphere is free to rotate about an axis passing through its Centre. Which of the two will acquire greater angular speed after a given time.
Answers
Answered by
2
Hii friend,
● Answer - Solid sphere
● Explaination-
Rotational torque can be calculated by,
τ = I × α
α = τ/I
For hollow cylinder, I1 = MR^2
α1 = τ/(MR^2) ...(1)
For solid sphere, I2 = 2/5 MR^2
α2 = τ/(2/5 MR^2) ...(2)
τ = same/constant
Dividing (2) by (1),
α2/α1 = (MR^2)/(2/5 MR^2)
α2/α1 = 5/2
Thus angular acceleration of solid sphere is 5/2 times that of hollow cylinder.
Hope that is useful...
● Answer - Solid sphere
● Explaination-
Rotational torque can be calculated by,
τ = I × α
α = τ/I
For hollow cylinder, I1 = MR^2
α1 = τ/(MR^2) ...(1)
For solid sphere, I2 = 2/5 MR^2
α2 = τ/(2/5 MR^2) ...(2)
τ = same/constant
Dividing (2) by (1),
α2/α1 = (MR^2)/(2/5 MR^2)
α2/α1 = 5/2
Thus angular acceleration of solid sphere is 5/2 times that of hollow cylinder.
Hope that is useful...
Similar questions